Problem 1052

Erdős Problem #1052: declared status 'open'. Formalized: yes. A unitary divisor of $n$ is $d\mid n$ such that $(d,n/d)=1$. A number $n\geq 1$ is a unitary perfect number if it is the sum of its unitary divisors (aside from $n$ itself). Are there only finite many unitary perfect numbers? Prize: $10. OEIS: A002827. Tags: number theory.